In wireless communication, certain advantages are offered by the use of multiple antenna elements for transmission, whether with one or with more than one receiving antenna element. These advantages include the potential to mitigate fading effects, and the potential to increase data transmission rates in a propagation channel of given characteristics.
A variety of schemes have been proposed for modulating data to be transmitted from a multiple-element array. In some of these schemes, referred to generally as space-time modulation, the data are transmitted in the form of codewords distributed in space—i.e., across the antenna array—and in time. Such a codeword comprises a plurality of complex-valued amplitudes modulated onto a carrier wave.
Within a given time interval, referred to as a symbol interval, a complex amplitude (which might be zero) is transmitted from each element of the antenna array. Conversely, at each element of the array, a sequence of amplitudes is transmitted over a succession of symbol intervals. The concurrent transmission of amplitudes from the elements of the array during one symbol interval is referred to as a channel use.
A codeword of the kind described above can be represented by a matrix. The respective entries of the matrix are proportional to the complex amplitudes to be transmitted. Each column of the matrix corresponds, e.g., to a respective transmitting antenna, and each row corresponds, e.g., to a respective symbol interval.
A variety of schemes have also been proposed for recovering the transmitted data from signals received by a single receiving antenna or a multiple-element receiving antenna array. Mathematical models of the propagation channel between the transmitting and receiving antennas generally include a matrix of channel coefficients, each such coefficient relating the amplitude received at a given element of the receiving array to the amplitude transmitted from a given element of the transmitting array. In some of the known reception schemes, the channel coefficients are assumed to be known, exemplarily from measurements made using pilot signals.
When the channel coefficients are known, methods of signal recovery can be used that effectively invert the channel matrix. Both direct and indirect methods are known for effectively inverting the channel matrix. Among the indirect methods are Maximum Likelihood (ML) detectors. Given an estimate of the channel matrix and a received signal, an ML detector computes a likelihood score for each of a plurality of candidate codewords, and selects that candidate codeword that yields the highest score. Because of noise and uncertainties in the channel coefficients due to fading, received signals are generally corrupted to a greater or lesser extent. Thus, it is advantageous to use codewords for which the likelihood scores have high discriminating power, even in the presence of fading and noise.
One known method of space time modulation is V-BLAST. In V-BLAST, an initial stream of data is apportioned into separate sequences of amplitudes, each of which is independently transmitted from one of the transmitting antenna elements. In effect, the codeword can be represented by a row vector having M entries, where M is the number of transmitting antennas. The single row represents a single symbol interval. Typically, a new codeword is transmitted in each symbol interval. The independent sequence of amplitudes transmitted by each antenna can be referred to as a substream because it contains a respective subset of the data in the initial data stream.
Several schemes have been described for recovering V-BLAST signals. Some such schemes use ML detectors. According to another such scheme, the entries of the transmitted vector are recovered one-by-one, with each successive recovery utilizing the results of the previous recoveries. One example of such a scheme is described in the co-pending U.S. patent application Ser. No. 09/438,900, filed Nov. 12, 1999 by B. Hassibi under the title “Method and Apparatus for Receiving Wireless Transmissions Using Multiple-Antenna Arrays,” and commonly assigned herewith.
V-BLAST is advantageous in that it can be used for communication at relatively high data rates without excessive computational complexity in the decoding of the received signals. However, the decoding schemes that offer the lowest complexity require that the number N of receiving antennas must equal or exceed the number M of transmitting antennas. Such a requirement is disadvantageous when, for example, a large installation such as a base station is transmitting to a small installation such as a hand-held mobile wireless terminal.
Another method of space time modulation is described in S. M. Alamouti, “A simple transmitter diversity scheme for wireless communications,” IEEE J. Sel. Area Comm. (October 1998) 1451-1458. In the Alamouti scheme, each codeword is distributed over two transmit antennas and two symbol intervals. Each codeword is determined by two distinct complex amplitudes, each belonging to a respective substream. In the first symbol interval, one of the amplitudes is transmitted from the first antenna, and the other amplitude is transmitted from the second antenna. In the second symbol interval, the complex amplitudes are interchanged between the two antennas, one of the complex amplitudes changes sign, and the complex conjugates of the resulting amplitudes are transmitted. Significantly, when a codeword of this kind is expressed in the form of a matrix, the matrix has orthogonal columns.
One drawback of the Alamouti scheme is that it makes the most efficient use of the theoretical information capacity of the propagation channel only when there is a single receiving antenna. The channel capacity is used less efficiently when further receiving antennas are added. Thus, gains that might otherwise be expected in data rate and fading resistance from multiple-antenna receiving arrays are not fully realized.
Extensions of the Alamouti scheme to more than two transmitting antennas and more than two symbol intervals per codeword are also known. The Alamouti scheme and its extensions are referred to generally as orthogonal designs because the matrices that represent the codewords are required to be orthogonal; that is, each column of such a matrix is orthogonal to every other column of the matrix. A further requirement of orthogonal designs is that for a matrix to represent a codeword, all columns of the matrix must have the same energy. In this regard, the “energy” of a column is the scalar product of that column with its complex conjugate.
Until now, there has been an unmet need for a space-time modulation scheme that can handle high data rates with relatively low decoding complexity and that uses the potentially available channel capacity with relatively high efficiency for any combination (M, N) of transmission and reception antennas.